In order to compute the SGWB produced by the mergers of unresolved binaries, we need an expression for their merger rate. Our derivation relies on the assumption that PBH binaries formed by tidal capture in very dense halos during the matter dominated era. However, we note that other scenarios exist where binaries can form in the early Universe [1]}, [2]}For the effects of different assumptions on the mechanism of binary formation on the SGWB, see Ref. [3]}, which appeared on the arXiv simultaneously to this paper. We note that, although their overall findings qualitatively agree with ours, the \(\Omega _{\rm GW}\)  they compute is quantitatively different due to the use of a slightly different formula for the computation of the SGWB, which does not include the merger and ringdown phases.
